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wlad13 [49]
2 years ago
6

May I also have an explanation?

Mathematics
1 answer:
Ilia_Sergeevich [38]2 years ago
3 0
First start with the squares we know that they have four equal sides. This means that all of the square sides are 10.
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Use the substitution method to solve the system of equations
PilotLPTM [1.2K]

You solve the substitution method to solve a system of equality by expressing one variable in terms of the other using one equation, and then plugging this expression in the other(s).

In this case, the first equation gives us a way to express n in terms of m. So, we can replace every occurrence of n in the second equation with the given formula.

The result is

14m+2n=-8 \iff 14m+2(-7m-4)=-8 \iff 14m-14m-8=-8 \iff -8=-8

So, the second equation turned to be an equality, i.e. an equation where both sides are the same.

This implies that the system has infinitely many solutions, because every couple (n,m) such that n=-7m-4 is a solution to the system, because it satisfies both equations: the first is trivially satisfied, whereas the second is an identity, and as such is satisfied by any value of the variable.

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2 years ago
Which statements about the graph of the function f(x) = –x2 – 4x + 2 are true? Check all that apply.
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3 years ago
Folding a rectangle along one diagonal results in a shape whose area is 2/3 that of the original
Charra [1.4K]

Answer:

  • 60°

Step-by-step explanation:

<em>Refer to attached picture</em>

Given rectangle ABCD. Its folded shape is given as well.

It has sides a and b and diagonal d, with the angle BCD marked as α.

We need to find the value of angle AOC or BOD.

This is going to be 2α, which is easy to find out. BOD is cut by the angle bisector, each of the angles is α.

Let the area of the rectangle is A, then the folded shape has area 2/3A.

<u>The area of rectangle ABCD:</u>

  • A = ab

<u>From the triangle CBD we get:</u>

  • a/d = sin α ⇒ a = d sin α
  • b/d = cos α ⇒ b = d cos α

<u>Then</u>

  • A = d sin α * d cos α = d²sin α cos α

Now, lets find the area of the folded shape.

It is the area of the rectangle minus the area of the triangle CMB as this part  is lost as part of overlap.

<u>Area of the triangle:</u>

  • A = 1/2dh

<u>Since h/(d/2) = tan α ⇒ h = 1/2d tan α, the area is:</u>

  • A = 1/2d*1/2d tan α = 1/4d² tan α

<u>We have the difference of the areas which is 1/3 of the area of the rectangle:</u>

  • 1/3(d²sin α cos α) = 1/4d² tan α
  • sin α cos α = 3/4 tan α
  • sin α cos α = 3/4 sin α / cos α
  • cos² α = 3/4
  • cos α = √(3/4)
  • cos α = √3/2
  • α = arccos (√3/2)
  • α = 30°

<u>The acute angle formed by the two diagonals of the rectangle is:</u>

  • 2α = 2*30° = 60°

3 0
2 years ago
Find the value of x
klio [65]
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3 0
3 years ago
Read 2 more answers
NEED HELP:
PSYCHO15rus [73]

Answer:

The radius is approx. 7.5

Let me know if it helps or if I got anything wrong!

Step-by-step explanation:

To find the circumference, you need to multiply the diameter by pi (3.14)

And for vice versa, just divide.

Since we don't know the diameter nor radius, we need to divide the Circumference (C) by pi (3.14)

47/3.14=14.968

Which is rounded up to 15.

We have now found the diameter.

We also know that the radius is half of the diameter

15/2=7.5

7 0
2 years ago
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